How real electric motors work - School of Physics - The University of ...

The sketch and circuit show a step-up transformer. To make a step-down transformer, one only has to put the source on the right and
the load on the left. ( Important safety note: for a real transformer, you could only 'plug it in backwards' only after verifying that the
voltage rating were appropriate.) So, how does a transformer work?
The core (shaded) has high magnetic permeability, ie a material that forms a magnetic field much more easily than free space does, due
to the orientation of atomic dipoles. (In the photograph, the core is laminated soft iron.) The result is that the field is concentrated
inside the core, and almost no field lines leave the core. If follows that the magnetic fluxes φ through the primary and secondary are
approximately equal, as shown. From Faraday's law, the emf in each turn, whether in the primary or secondary coil, is −dφ/dt. If we
neglect resistance and other losses in the transformer, the terminal voltage equals the emf. For the N p turns of the primary, this gives
V p = − N p .dφ/dt .
For the N s turns of the secondary, this gives
V s = − N s .φ/dt
Dividing these equations gives the transformer equation
V s /V p = N s /N p = r.
where r is the turns ratio. What about the current? If we neglect losses in the transformer (see the section below on efficiency), and if
we assume that the voltage and current have similar phase relationships in the primary and secondary, then from conservation of
energy we may write, in steady state:
Power in = power out,
so
V p I p = V s I s ,
whence
I s /I p = N p /N s = 1/r.
So you don't get something for nothing: if you increase the voltage, you decrease the current by (at least) the same factor. Note that, in
the photograph, the coil with more turns has thinner wire, because it is designed to carry less current than that with fewer turns.